Convergence of Alexandrov spaces and spectrum of Laplacian

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Abstract

Denote by script A sign(n) the family of isometry classes of compact n-dimensional Alexandrov spaces with curvature ≥ -1, and λk(M) the kth eigenvalue of the Laplacian on M ∈ script A sign(n). We prove the continuity of λk : script A sign(n) → R with respect to the Gromov-Hausdorff topology for each k, n ∈ N, and moreover that the spectral topology introduced by Kasue-Kumura [7], [8] coincides with the Gromov-Hausdorff topology on script A sign(n).

Original languageEnglish
Pages (from-to)x-15
JournalJournal of the Mathematical Society of Japan
Volume53
Issue number1
DOIs
Publication statusPublished - 2001 Jan

Keywords

  • Alexandrov space
  • Eigenvalue
  • Laplacian
  • Spectrum
  • The Gromov-Hausdorff distance
  • The spectral distance

ASJC Scopus subject areas

  • Mathematics(all)

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